On a multidimensional Volkenborn integral and higher order Bernoulli numbers
- 1 February 2002
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 65 (1) , 59-71
- https://doi.org/10.1017/s0004972700020062
Abstract
In this paper, using a multidimensional Volkenborn integral, we give ap-adic expression of the higher order Bernoulli numbers. This shows immediately the relation to the sums of products of the ordinary Bernoulli numbers of Dilcher in 1996. We also consider the Mahler expansion of severalp-adic variables function, and give some examples.Keywords
This publication has 12 references indexed in Scilit:
- A Course in p-adic AnalysisPublished by Springer Nature ,2000
- Congruences for Bernoulli, Euler, and Stirling NumbersJournal of Number Theory, 1999
- Introduction to Cyclotomic FieldsPublished by Springer Nature ,1997
- Sums of Products of Bernoulli NumbersJournal of Number Theory, 1996
- Congruences ofp-adic Integer Order Bernoulli NumbersJournal of Number Theory, 1996
- Congruences and Recurrences for Bernoulli Numbers of Higher OrderThe Fibonacci Quarterly, 1994
- p-adic Numbers, p-adic Analysis, and Zeta-FunctionsPublished by Springer Nature ,1984
- P-adic AnalysisPublished by Cambridge University Press (CUP) ,1980
- The p-Adic Log Gamma Function and p-Adic Euler ConstantsTransactions of the American Mathematical Society, 1977
- Vorlesungen über DifferenzenrechnungPublished by Springer Nature ,1924